Stresses at spoke elbows

Ben C said:

But the term has another technical sense to describe stresses inside a
material that remain after plastic bending and spring-back. When you
bend a wire, the material near the skin goes through bigger angle
changes than the stuff nearer the centre. After the wire springs back
(the bend bounces out a bit), you're left with the unyielded interior
pushing elastically against the yielded exterior.

Note that these stresses are compressive on the outside of the bend and
tensile on the inside, so if present in a spoke would actually mitigate
the tensile stress on the outside of the elbow that may remain after
bending.

Only if the spoke was relaxed. If a spoke is bent and held in the bent
position, the skin forces are the same as the core forces.

Quoted message said:

The spoke-toasting experiment of Carl Fogel indicated that these
residual stresses are relieved at tensions below what you expect in a
normal wheel anyway.

Carl heated a (relaxed) previously bent spoke. Heating will relieve
internal stresses, but a spoke heated with a torch will heat from the
outside in, relaxing the skin before the core. In this case, the core
forces will bend the spoke before they also relax.

Quoted message said:

Residual stress of a similar kind to that remaining after spring-back
may remain in spokes after fabrication, and here we get into the
descriptions of the fabrication process. It would seem that the
spoke-toasting is good evidence that these stresses, if present, are
relieved anyway by normal tensioning, but there are also arguments
people have made against that.

Carl's experiment also unbent the spoke, reducing the core elastic
forces, so smaller changes with heating would be expected.

Quoted message said:

A simple test for presence of residual stress from fabrication is the
chloride test.

It is neither simple nor a sure fire indicator. Stress corrosion
cracking is dependent on the alloy (none of the spoke manufacturers
reveal theirs). It involves high temperature solution exposure for long
periods (ASM G36). SCC cracks often have very low growth rates (in the
order of years per mm). The cracks are typically small intergranular and
are only visible under magnification, often only after sectioning and
polishing.

I was inspired by this article:
http://www.lanl.gov/residual/

to think about using a similar method to reveal residual stresses.

I bent a spoke sharply (small radius on a vise). I clamped the small
(~1"😉 part in the vise so that the remainder extended vertically. I
fixed a indicator behind the spoke so I could measure deflection of the
vertical part (~10"😉. Using a Dremel tool with a very thin cutoff disk
at low rpm, I began to remove material from the outside of the bend. I
did this slowly and gradually over the course of about 10 min., until I
had removed about 90% of the cross section.

I found that removing material from the outside of the bend cause the
spoke to bend more (smaller angle). The change was small, perhaps 2-3mm
movement at the end. I repeated the experiment with the same result.
Next, I tried the same experiment only removing material from the inside
of the bend. This time I saw the same magnitude of change, but in the
opposite direction, a slight unbending (the angle grew larger).

Lastly, I repeated the experiment with an unused DT spoke. I clamped
just the head in the vise so the elbow would be exposed and cut a slit
on the outside of the bend. The spoke bent more (to a smaller angle),
much the same as the bends I had made myself. My conclusion is that the
DT bend has the same residual as mine.

I'd like someone else to try this to confirm my results.

For the record, I torch-heated a 90 deg. bend and saw a similar amount
of deflection as in my test (a few mm) in the same direction Carl did.

On Wed, 10 Jan 2007 06:17:31 -0600, Ben C <[email hidden]> wrote:

[snip]

Dear Ben,

Thanks for the summary.

Two missing details may be important.

The spoke holes in the flange are counterbored on both ends, so at the
scale of a spoke, the lip of the spoke hole is pre-curved to an
appreciable degree.

But I suspect that even with the help of the counterbore, the outer
spokes rarely (if ever)lie flat on the hub flange for their whole
length.

Here's your diagram modified:

s\HHHHHHH/ <--undamaged counter-bore
ssssssss
s/HHHHH\s <--some bedding-gouging
\s
\s
|s
|.s
|..s <--spoke still curves off flange
|..s . = gap, the d of Ben's diagram
|.s
|s
|s <--now bent flat against flange
|s by hand for a long stretch
|s
s
s
s
rim

That is, the spoke never lies flat on the hub flange near the elbow.
Short of using a hammer and steel mandrel, bending to adjust the spoke
line always leaves a little space where the elbow curves away from the
hub, the gap d that interests you.

Here's a diagram from p. 80 of "The Bicycle Wheel," 3rd edition,
showing the ever-present gap d:

http://i16.tinypic.com/2qdzpt4.jpg

The idealized diagram doesn't show the flange counterboring--note that
the artist has the angled spoke head sitting above the idealized
right-angle hole through the flange.

But the diagram does show the additional slight complication of the
spoke cocking in the hole through the flange, due to the slight
clearance.

Cheers,

Carl Fogel

Ben C said:

Both spoke bending and hub deformation
--------------------------------------

As tension is gradually applied to the spoke, at first it starts to bend
a bit, but as the spoke's exit line approaches parallel to the force
line, the moment becomes too small for it to continue to bend, and the
spoke elbow is held at yield stress.

In this scenario, as the tension is increased further, the pressure on
the inside of the hub starts to deform the exit hole, and the spoke
continues to pull closer to the flange, not by bending but by cutting
into the hub slightly.

This reduces the distance "d" even further, which means that the stress
at the spoke elbow actually reduces, even though the applied force is
still growing slowly as we wind the nipple.

You are speculating about the "stress at the spoke elbow", and there are
several stresses at work.

The only important thing is, that after tensioning, the spoke (depending
on whether its initial angle was too big or too small) is either trying
to open up or close at the bend. In the first case (too small an initial
bend angle) the tension from bending is on the inside, in the second
case, on the outside. Tension is the only important bending stress
because it gets added to the axial tension.

If spokes break (fatigue) on the outside of the bend, it can only mean
that the initial angle was too great. That the spoke doesn't lie flat to
the (angled) flange is only a symptom of that. In the other case (too
small an angle), lying flat to the flange tells you nothing.

When you momentarily increase the spoke tension by a large amount during
stress relief, you yield the areas at or near (tensile) yield. It
doesn't matter if they are on the inside or outside of the bend. It has
the same effect (for those small regions) of briefly increasing the bend
in the direction it wants to go (to be perfect), yielding material
further in that direction and (when released) lowering the tensile
stress there. This is pretty much what would occur if you could just
bend the spoke further in the direction it wanted to go.

If outbound spokes show a change from obtuse (factory) to acute after
tensioning, it's only because the initial angle was too great.
Correcting the spoke line (at the hub, after tensioning) can't
completely eliminate the discrepancy; the tensile stresses will be on
the outside of the elbows, and if not stress relieved, the spokes will
fail there.

Peter Cole said:

Ben C wrote:

Quoted message said:

It is neither simple nor a sure fire indicator. Stress corrosion
cracking is dependent on the alloy (none of the spoke manufacturers
reveal theirs). It involves high temperature solution exposure for long
periods (ASM G36). SCC cracks often have very low growth rates (in the
order of years per mm). The cracks are typically small intergranular and
are only visible under magnification, often only after sectioning and
polishing.

FWIW when I first started with the Aerospace company I worked for, I
did a bunch of tests on spokes, (1) Including stress corrosion and
micro sectioning. To the best of my ability to test (no scanning
electron microscope or gas chromatograph) the DT spokes I looked at
were 304, rockwell / uts / mag-perm / sheer / acid etch etc. all
pointed in that direction and since it is the most common grade of
stainless used and relatively cheap I am reasonably confident that I am
correct.

but as it was 12+ years ago now the odds of the test pieces still
being around are slim..

As an aside and since I can't provide the test pieces or results
anymore, the grain structure and the stress corrosion results supported
the idea that residual stress existed at the elbow.. that stress wanted
the spoke to straighten.

(1) and one or two tests of hubs, welds cranks etc. as I used up the
extra bits I acquired over the years.

Peter Cole said:

Ben C said:

But the term has another technical sense to describe stresses inside a
material that remain after plastic bending and spring-back. When you
bend a wire, the material near the skin goes through bigger angle
changes than the stuff nearer the centre. After the wire springs back
(the bend bounces out a bit), you're left with the unyielded interior
pushing elastically against the yielded exterior.

Note that these stresses are compressive on the outside of the bend and
tensile on the inside, so if present in a spoke would actually mitigate
the tensile stress on the outside of the elbow that may remain after
bending.

Only if the spoke was relaxed. If a spoke is bent and held in the bent
position, the skin forces are the same as the core forces.

Yes, that was what I was trying to clarify, I think-- the distinction
between applied stress at the elbow and the sort of residual stresses
you get when you bend and allow to spring back.

Quoted message said:

Quoted message said:

The spoke-toasting experiment of Carl Fogel indicated that these
residual stresses are relieved at tensions below what you expect in a
normal wheel anyway.

Carl heated a (relaxed) previously bent spoke. Heating will relieve
internal stresses, but a spoke heated with a torch will heat from the
outside in, relaxing the skin before the core. In this case, the core
forces will bend the spoke before they also relax.

Yes isn't that the principle-- if you heat it and it unbends a bit that
means you have residual stresses, or have I misunderstood?

[snip]

Quoted message said:

Quoted message said:

A simple test for presence of residual stress from fabrication is the
chloride test.

It is neither simple nor a sure fire indicator. Stress corrosion
cracking is dependent on the alloy (none of the spoke manufacturers
reveal theirs). It involves high temperature solution exposure for long
periods (ASM G36). SCC cracks often have very low growth rates (in the
order of years per mm). The cracks are typically small intergranular and
are only visible under magnification, often only after sectioning and
polishing.

So I guess you don't hold out much hope for the couple of samples I've
left in a jar of salt water...

[snip]

Quoted message said:

Lastly, I repeated the experiment with an unused DT spoke. I clamped
just the head in the vise so the elbow would be exposed and cut a slit
on the outside of the bend. The spoke bent more (to a smaller angle),
much the same as the bends I had made myself. My conclusion is that the
DT bend has the same residual as mine.

Excellent result!

Actually that test could possibly even be done in an assembled wheel,
before and after stress-relief.

Ben C said:

On 2007-01-10, Peter Cole <[email hidden]> wrote:

Quoted message said:

Quoted message said:

Quoted message said:

The spoke-toasting experiment of Carl Fogel indicated that these
residual stresses are relieved at tensions below what you expect in a
normal wheel anyway.

Carl heated a (relaxed) previously bent spoke. Heating will relieve
internal stresses, but a spoke heated with a torch will heat from the
outside in, relaxing the skin before the core. In this case, the core
forces will bend the spoke before they also relax.

Yes isn't that the principle-- if you heat it and it unbends a bit that
means you have residual stresses, or have I misunderstood?

As I said, the tensioning unbent the spoke, removing most of the
stresses that way. The spokes in wheels remain bent.

Quoted message said:

[snip]

Quoted message said:

Quoted message said:

A simple test for presence of residual stress from fabrication is the
chloride test.

It is neither simple nor a sure fire indicator. Stress corrosion
cracking is dependent on the alloy (none of the spoke manufacturers
reveal theirs). It involves high temperature solution exposure for long
periods (ASM G36). SCC cracks often have very low growth rates (in the
order of years per mm). The cracks are typically small intergranular and
are only visible under magnification, often only after sectioning and
polishing.

So I guess you don't hold out much hope for the couple of samples I've
left in a jar of salt water...

[snip]

Quoted message said:

Lastly, I repeated the experiment with an unused DT spoke. I clamped
just the head in the vise so the elbow would be exposed and cut a slit
on the outside of the bend. The spoke bent more (to a smaller angle),
much the same as the bends I had made myself. My conclusion is that the
DT bend has the same residual as mine.

Excellent result!

I'm not sure it's excellent. It's a data point that seems to answer
whether spokes have residual stresses from manufacture. I'll wait for
others to comment/confirm.

Quoted message said:

Actually that test could possibly even be done in an assembled wheel,
before and after stress-relief.

I don't see how. I wouldn't want to cut a 90% slit through a loaded
spoke, nor do I think that would show anything.

Quoted message said:

Peter Cole said:

Ben C wrote:

Quoted message said:

It is neither simple nor a sure fire indicator. Stress corrosion
cracking is dependent on the alloy (none of the spoke manufacturers
reveal theirs). It involves high temperature solution exposure for long
periods (ASM G36). SCC cracks often have very low growth rates (in the
order of years per mm). The cracks are typically small intergranular and
are only visible under magnification, often only after sectioning and
polishing.

FWIW when I first started with the Aerospace company I worked for, I
did a bunch of tests on spokes, (1) Including stress corrosion and
micro sectioning. To the best of my ability to test (no scanning
electron microscope or gas chromatograph) the DT spokes I looked at
were 304, rockwell / uts / mag-perm / sheer / acid etch etc. all
pointed in that direction and since it is the most common grade of
stainless used and relatively cheap I am reasonably confident that I am
correct.

but as it was 12+ years ago now the odds of the test pieces still
being around are slim..

As an aside and since I can't provide the test pieces or results
anymore, the grain structure and the stress corrosion results supported
the idea that residual stress existed at the elbow.. that stress wanted
the spoke to straighten.

(1) and one or two tests of hubs, welds cranks etc. as I used up the
extra bits I acquired over the years.

Thanks, another data point (in the same direction).

On 2007-01-10, Peter Cole <[email hidden]> wrote:
[snip]

Quoted message said:

Quoted message said:

Actually that test could possibly even be done in an assembled wheel,
before and after stress-relief.

I don't see how. I wouldn't want to cut a 90% slit through a loaded
spoke, nor do I think that would show anything.

If the outside elbow of an outbound spoke was under tension, and you cut
a little slit at the outside of the bend, would it not tear open a bit?

I mean the slit tear open, the elbow bend would become more acute. The
idea is you make the material a bit thinner so it starts to strain
visibly if it's under stress.

Quoted message said:

On Wed, 10 Jan 2007 06:17:31 -0600, Ben C <[email hidden]> wrote:

[snip]

Dear Ben,

Thanks for the summary.

Two missing details may be important.

The spoke holes in the flange are counterbored on both ends, so at the
scale of a spoke, the lip of the spoke hole is pre-curved to an
appreciable degree.

But I suspect that even with the help of the counterbore, the outer
spokes rarely (if ever)lie flat on the hub flange for their whole
length.

Here's your diagram modified:

s\HHHHHHH/ <--undamaged counter-bore
ssssssss
s/HHHHH\s <--some bedding-gouging
\s
\s
|s
|.s
|..s <--spoke still curves off flange
|..s . = gap, the d of Ben's diagram
|.s
|s
|s <--now bent flat against flange
|s by hand for a long stretch
|s
s
s
s
rim

This is a much better diagram. Note that "d" here doesn't work in quite
the same way as in my simplified diagram. The general principle is still
about right: that the bigger d is, the less tension you require to keep
the bend yielding, and that as d tends to zero the tension required
tends to the maximum (the amount you'd need to stretch the spoke
plastically). But straightening the hook of the question mark is rather
more difficult geometry than the simple moment F x d in the simplified
diagram.

Ben C said:

On 2007-01-10, Peter Cole <[email hidden]> wrote:
[snip]

Quoted message said:

Quoted message said:

Actually that test could possibly even be done in an assembled wheel,
before and after stress-relief.

I don't see how. I wouldn't want to cut a 90% slit through a loaded
spoke, nor do I think that would show anything.

If the outside elbow of an outbound spoke was under tension, and you cut
a little slit at the outside of the bend, would it not tear open a bit?

I mean the slit tear open, the elbow bend would become more acute. The
idea is you make the material a bit thinner so it starts to strain
visibly if it's under stress.

Try it and get back to me.

In article <[email hidden]>,

Peter Cole said:

I bent a spoke sharply (small radius on a vise). I clamped the small
(~1"😉 part in the vise so that the remainder extended vertically. I
fixed a indicator behind the spoke so I could measure deflection of
the vertical part (~10"😉. Using a Dremel tool with a very thin cutoff
disk at low rpm, I began to remove material from the outside of the
bend. I did this slowly and gradually over the course of about 10
min., until I had removed about 90% of the cross section.

I found that removing material from the outside of the bend cause the
spoke to bend more (smaller angle). The change was small, perhaps
2-3mm movement at the end. I repeated the experiment with the same
result. Next, I tried the same experiment only removing material from
the inside of the bend. This time I saw the same magnitude of change,
but in the opposite direction, a slight unbending (the angle grew
larger).

Lastly, I repeated the experiment with an unused DT spoke. I clamped
just the head in the vise so the elbow would be exposed and cut a
slit on the outside of the bend. The spoke bent more (to a smaller
angle), much the same as the bends I had made myself. My conclusion
is that the DT bend has the same residual as mine.

I'd like someone else to try this to confirm my results.

Well, the next step would be to take a spoke that has been treated to
Jobst stress-relieving method and see if it behaves the same way, and to
take a spoke that has been built into a wheel but not stress-relieved
and see if that too behaves the same way. If Jobst's stress relieving
method works, it would be reasonable to predict that the angle of the
spoke would change somewhat less on the tensioned-but-not-relieved
spoke, and would change much less on the stress-relieved spoke.

Ben C said:

A recent thread entitled "I fixed a broken spoke" about various things
including stresses at spoke elbows got so long it starting disappearing
off the ends of people's newsreaders. But since some people are still
interested in it it was suggested I should do a summary.

I'll try to keep it as short I can. No attributions, but most of the
material is originally from either Jobst or jim beam. Any
misrepresentations are unintentional.

Stress and stress relief
------------------------

This is a picture of a spoke sitting in a hole in a hub flange.

sHHHHHH <--- Hub
sssssssssss
sHHHHHH s
s
<-d->s <--- Spoke
s
s
s
RIM

If you pull the spoke along its axis towards the rim either the spoke
bends a bit more at the elbow, or the spoke cuts into the body of the
hub, or a bit of both.

We'll consider the first possibility in isolation first, so assume for
now that the hub hole is not deformable at all (this is pretty much the
case for a steel hub).

In the diagram the perpendicular distance from the spoke to the hub
flange has been labelled <-d->. The longer this distance, the lower the
force required to bend the spoke. The product of F and d is called a
"moment".

As this distance approaches zero, the force required to bend the spoke
absolutely flush with the flange approaches the force that would be
required to stretch a spoke plastically-- a force that's significantly
higher than spoke tension in a finished bicycle wheel.

In other words, to achieve this situation:

sHHHHHH
ssssssss
sHHHHHHs
s
s
s
s

just by pulling on the spoke would take a LOT of force.

Suppose you pull on the spoke with a force that gradually increases from
zero up to about normal tension, corresponding with screwing up the
nipple as you build the wheel. As the spoke bends towards the hub the
distance "d" gets shorter, and it gets harder to bend the spoke. Soon
you reach an equilibrium position in which the applied force holds the
bend where it is, but is unable to make it any tighter.

This applied force will hold the outside of the bend at just about the
yield stress of the material-- after all it's just been yielding (i.e.
bending) and you haven't relaxed the force, so it will be kept at yield.

So the spoke will not be quite flush with the flange, but some distance
"d" from it. How big is "d" exactly? I don't know for sure, I should
work it out, it isn't hard, and it's an important detail.

If you rode away on the bike like that you would expect rapid fatigue at
the spoke elbows since steel, like many materials, doesn't last very
long if it's cycled (repeatedly tensioned and relaxed again) at a high
mean stress.

But if you pull on the spoke a bit harder still and let go of it again,
you can plastically stretch the outside of the elbow a little bit
further, with the result that when you relax that momentary overload,
the outside of the elbow is left at a much lower stress.

This improves the life of the wheel, and is called "mechanical stress
relief".

Hub deformation
---------------

We've all seen the indentations around the exit holes of used hubs, and
we know that hubs are often made of aluminium that is softer than the
stainless steel used for spokes.

So what if the elbow doesn't bend at all, but instead just digs itself
into the hub a bit as it's pulled flush to the flange by normal
tensioning, and perhaps by some overload applied deliberately during the
build?

When you take an old wheel apart, you can often tell which spokes were
"inbound" and which were "outbound" by the different elbow bends, which
implies that the elbows _did_ bend as they were pulled towards the rim.
But the picture is confused because many builders bend the elbows
manually with their thumb or a crank-arm (which takes relatively little
force to do because of the position and direction in which the force is
applied).

We have seen inbound and outbound spokes from one poster, who advocates
against premature elbow-thumbing, that showed a barely perceptible
difference in elbow angle.

Of course if the elbow doesn't bend, or the hub is too soft to support
the force required to hold a bend in the elbow, there's no reason to
believe that the outside of the elbow will remain at yield stress after
spoke tensioning.

Both spoke bending and hub deformation
--------------------------------------

As tension is gradually applied to the spoke, at first it starts to bend
a bit, but as the spoke's exit line approaches parallel to the force
line, the moment becomes too small for it to continue to bend, and the
spoke elbow is held at yield stress.

In this scenario, as the tension is increased further, the pressure on
the inside of the hub starts to deform the exit hole, and the spoke
continues to pull closer to the flange, not by bending but by cutting
into the hub slightly.

This reduces the distance "d" even further, which means that the stress
at the spoke elbow actually reduces, even though the applied force is
still growing slowly as we wind the nipple. The moment Fd gets smaller
because although F is increasing, d is reducing more rapidly. In other
words, as the pivot around which we're twisting the spoke deforms, the
spoke unbends a bit.

We said at the start that to pull the spoke completely flush to the
flange around a non-deformable pivot would take significantly more spoke
tension than we ever get in a bicycle wheel.

So one possibility is that the spoke doesn't end up completely flush.
Another is that hub-hole deformation allows the spoke to pull flush, and
a consequence of this is that the spoke elbow does not remain at yield
after tensioning. There may still be some stress at the elbow though--
how far the bend gets relaxed depends on the extent of each of these
effects.

Spoke Line Correction
---------------------

So far we've been talking about building a wheel by just putting the
spokes in and tightening them up, followed perhaps by some momentary
overload process to relieve bending stress at the elbow.

But many builders push the spokes towards the flange earlier in the
process with their thumbs or old crank arms. If the elbow angle can be
made just right before the spoke is tensioned, then it won't need to
bend during the build, and we can expect the spoke to lie flush to the
flange when we're finished without requiring either hub-hole deformation
or yield stress at the elbow.

But is it possible to get the angle just right? In theory, no, on the
grounds that you cannot bend the spoke further than flush (the flange is
in the way), and that after you bend it it's always going to bounce back
a little bit.

In practice I'm not so sure. If the spoke is still quite loose, it may
not be sitting in quite its final position in the hub hole. If you can
hinge it back a bit before bending it, it seems at least possible that
you should be able to exceed the angle of the flange.

Which is right?
---------------

We can be fairly sure that spoke tension cannot hold the bend at yield
for the small value of "d" implied by flushness, and therefore that if
the spoke really is truly flush when we've finished, the bend is no
longer at yield.

So is the spoke truly flush? How far away does it have to be for it to
be reasonable for normal spoke tension to hold the elbow at yield?

It's hard to say. Small differences in angles and lengths is all it
takes one way or the other. Furthermore the spoke may end up bent into a
kind of question-mark shape just where it exits the flange, meaning it
can lie flat a bit further away, requiring less tension to keep it
there, but making it look flush unless you inspect very carefully around
where it exits the hole. The tighter the radius of the question-mark's
hook, the more tension is required, although the geometry gets much more
complicated at this scale. Do we see hooks? What are their radii? It
would help to have a close look at a few wheels, especially ones that we
knew hadn't undergone manual spoke line correction, but even then it
would be hard to know exactly what to conclude.

A good argument against hub-hole deformation relaxing yield stress at
the elbow (or in any way mitigating the bending of the elbow) is that we
would expect any deformation of the hub to happen sooner rather than
later in the build process. As the wire first starts to sink into the
aluminium, the contact patch is a thin line on the surface of the spoke
which sinks in like a knife blade. But as more of the wire sinks in, the
size of the contact quickly grows, and the amount of compressed
aluminium pushing it back increases. By the time the spoke is getting
near the flange, it's already sunk in enough that the apparently soft
aluminium hub is effectively no longer deformable.

My own conclusion is that theory doesn't tell us for sure whether or not
the spoke elbow is kept at or close to yield by spoke tension. More
evidence is needed. Carl puts it best: "the spokes do whatever they do
regardless of our red herrings".

It also depends on the choice of components used, in particular the
length of the elbow shanks and the orientation of the hub holes, which
varies even between different recent hubs from the same manufacturer as
people have been discussing recently. The situation may be different in
different wheels.

We have good ancedotal evidence that temporarily overloading the spokes
after tensioning produces more durable wheels. We know that this process
would relieve tensile stress at the elbow if it were there, and that
that would improve fatigue life.

On the other hand the temporary overload may have other benefits. It may
be that it helps seat the spokes into the hub, it may just be that
temporarily underloading the spokes (a sideeffect of certain
temporary-overload procedures) takes out windup.

Or it may have no positive benefits at all. The anecdotal evidence it
does something useful is good, but as time goes by the components we buy
from the manufacturers change with quite significant differences in
materials, geometry and importantly surface finish which is known to be
highly significant in fatigue failure.

It's less clear how different processes of stress relieving could do any
harm, although I think mechanisms may have been suggested by which that
is possible. As far as I remember I think we're all pretty much agreed
that the "Mavic Method" is probably beneficial and unlikely to do any
harm.

"Residual stress"
-----------------

The bend stress that may exist at the spoke elbow after tensioning that
I've been describing is sometimes called "residual stress". I believe
this is the term used in Jobst's book _The Bicycle Wheel_.

This seems a reasonable thing to call it on the plain-English grounds
that it's residual (left-over after bending) and it's stress.

But the term has another technical sense to describe stresses inside a
material that remain after plastic bending and spring-back. When you
bend a wire, the material near the skin goes through bigger angle
changes than the stuff nearer the centre. After the wire springs back
(the bend bounces out a bit), you're left with the unyielded interior
pushing elastically against the yielded exterior.

Note that these stresses are compressive on the outside of the bend and
tensile on the inside, so if present in a spoke would actually mitigate
the tensile stress on the outside of the elbow that may remain after
bending.

The spoke-toasting experiment of Carl Fogel indicated that these
residual stresses are relieved at tensions below what you expect in a
normal wheel anyway.

But these are not the same "residual stresses" as the bend stress
remaining at the elbow that we've been talking about. However many of us
didn't realize that that was what we were talking about until quite late
in the day.

no, they're exactly the same kind of thing. the profile may be slightly
different because the bend radius is different, but the principle is
identical.

Quoted message said:

Is is correct to use the term "residual stress" for this bend stress
remaining at the elbow? I don't know, but I do know I promised Ed
Pirrero a 500-post flame war on the subject. So, gentlemen, in your own
time, start whenever you're ready.

Residual stress of a similar kind to that remaining after spring-back
may remain in spokes after fabrication, and here we get into the
descriptions of the fabrication process. It would seem that the
spoke-toasting is good evidence that these stresses, if present, are
relieved anyway by normal tensioning, but there are also arguments
people have made against that.

if there's residual stress at the elbow from manufacture, there's
residual stress at the elbow from manufacture. but presumption is not
any form of quantification. theory is that there's compressive [i.e.
fatigue mitigating] stress on the outside of spoke elbows, but they
still break there anyway - and they /don't/ break where tensile residual
stress is highest. since residual stress theory and observed failures
are not in accord, the role residual stress plays in spoke fatigue is at
best "unproven".

Quoted message said:

A simple test for presence of residual stress from fabrication is the
chloride test.

indeed.

all in all, from my first reading, a pretty decent summary. but i'll
have to get back to you if you want more detail. time limited.

Quoted message said:

Peter Cole said:

Ben C wrote:

Quoted message said:

It is neither simple nor a sure fire indicator. Stress corrosion
cracking is dependent on the alloy (none of the spoke manufacturers
reveal theirs). It involves high temperature solution exposure for long
periods (ASM G36). SCC cracks often have very low growth rates (in the
order of years per mm). The cracks are typically small intergranular and
are only visible under magnification, often only after sectioning and
polishing.

FWIW when I first started with the Aerospace company I worked for, I
did a bunch of tests on spokes, (1) Including stress corrosion and
micro sectioning. To the best of my ability to test (no scanning
electron microscope or gas chromatograph) the DT spokes I looked at
were 304, rockwell / uts / mag-perm / sheer / acid etch etc. all
pointed in that direction and since it is the most common grade of
stainless used and relatively cheap I am reasonably confident that I am
correct.

but as it was 12+ years ago now the odds of the test pieces still
being around are slim..

As an aside and since I can't provide the test pieces or results
anymore, the grain structure and the stress corrosion results

what did you use?

Quoted message said:

supported
the idea that residual stress existed at the elbow.. that stress wanted
the spoke to straighten.

(1) and one or two tests of hubs, welds cranks etc. as I used up the
extra bits I acquired over the years.

good to hear - someone that actually did testing!!! it would be great
if you could share more detail.

Peter Cole said:

It is neither simple nor a sure fire indicator. Stress corrosion cracking
is dependent on the alloy (none of the spoke manufacturers reveal theirs).

The Wheelsmith website < http://www.wheelsmith.com/index_files/wsspokes.htm

Quoted message said:

was talked about recently here. I noticed that they also use 304

stainless steel.

On Wed, 10 Jan 2007 20:53:36 -0900, "Andrew Lee"

whatsupandrewathotmaildotcom said:

Peter Cole said:

It is neither simple nor a sure fire indicator. Stress corrosion cracking
is dependent on the alloy (none of the spoke manufacturers reveal theirs).

The Wheelsmith website < http://www.wheelsmith.com/index_files/wsspokes.htm

Quoted message said:

was talked about recently here. I noticed that they also use 304

stainless steel.

Dear Andrew,

As a sidelight on what spokes are made of, Jobst pointed out the
change in spoke materials between the first and second edition of "The
Bicycle Wheel":

"In contrast to spokes tested for the first edition of this book,
these spokes withstood substantial elongation before failure,
indicating improved spoke materials."

Graphs in the first and second editions indicate that DT 2mm straight
stainless steel spokes tested in the 1st edition (1981) failed at ~700
lbs of stress and ~2.6 mm of strain, while DT 2mm straight stainless
steel spokes tested in the second edition (1988) failed at ~700 lbs of
stress again, but ~4.0 mm of strain.

Somehow the "stainless steel" in 2mm DT spokes became 50% stretchier.

There's also an obvious difference between the carbon steel and the
stainless steel spokes pulled to destruction in the first edition. The
carbon spokes have a sharp failure peak, while the stainless steel
spokes have much stretchier, more rounded failure curve.

Here's a crude comparison for the 2mm straight DT spokes in the two
editions:

1981 1981 1988
carbon stainless stainless
^ .. . . . . .
| / \ ' ' ' '
L / / '
B / / /
S
abcd abcdef abcdefgh
STRETCH-->

Cheers,

Carl Fogel

jim beam said:

Ben C wrote:

[snip]

Quoted message said:

Quoted message said:

The spoke-toasting experiment of Carl Fogel indicated that these
residual stresses are relieved at tensions below what you expect in a
normal wheel anyway.

But these are not the same "residual stresses" as the bend stress
remaining at the elbow that we've been talking about. However many of us
didn't realize that that was what we were talking about until quite late
in the day.

no, they're exactly the same kind of thing. the profile may be slightly
different because the bend radius is different, but the principle is
identical.

Residual stress from fabrication seems close enough to what Carl (and
more recently also Peter Cole) tested.

But those tests tell us nothing about _applied_ stress at the elbow due
to tension in the finished wheel. That's all I was saying.

jim beam said:

if there's residual stress at the elbow from manufacture, there's
residual stress at the elbow from manufacture. but presumption is not
any form of quantification. theory is that there's compressive [i.e.
fatigue mitigating] stress on the outside of spoke elbows, but they
still break there anyway - and they /don't/ break where tensile residual
stress is highest. since residual stress theory and observed failures
are not in accord, the role residual stress plays in spoke fatigue is at
best "unproven".

If we look at residual stresses and superimpose various applied stresses
we see the following:

Residual stress, going from inside to outside of the elbow:

T C T C

If we superimpose spoke tension:

T+ C- T+ C-

If we add stress relief momentary force:

T++ C-- T++ C--

Another case where the original angle is too small:

T C T C (residual)
T+ C- T+ C- (residual + spoke tension)
T++ C-- T+- C-+ (residual + tension + bending force)
T+++ C--- T+-+ C-+- (residual + tension + bending force + stress relief)

Another case where the original angle is too large:

T C T C (residual)
T+ C- T+ C- (residual + spoke tension)
T+- C-+ T++ C-- (residual + spoke tension + bending force)
T+-+ C-+- T+++ C--- (residual + spoke tension + bending force + stress
relief)

The above illustrates only directions, not magnitudes, but if we assume
"T++" and above will result in yield followed by a reduction in T, we
can see that stress relief is beneficial in all 3 cases. It is important
to remember that these stress regions have gradients and that the large
relative change in initial absolute compression will give absolute
tension, i.e. C--- ~= T+.

jim beam said:

Quoted message said:

Peter Cole said:

Ben C wrote:

Quoted message said:

It is neither simple nor a sure fire indicator. Stress corrosion
cracking is dependent on the alloy (none of the spoke manufacturers
reveal theirs). It involves high temperature solution exposure for long
periods (ASM G36). SCC cracks often have very low growth rates (in the
order of years per mm). The cracks are typically small intergranular and
are only visible under magnification, often only after sectioning and
polishing.

FWIW when I first started with the Aerospace company I worked for, I
did a bunch of tests on spokes, (1) Including stress corrosion and
micro sectioning. To the best of my ability to test (no scanning
electron microscope or gas chromatograph) the DT spokes I looked at
were 304, rockwell / uts / mag-perm / sheer / acid etch etc. all
pointed in that direction and since it is the most common grade of
stainless used and relatively cheap I am reasonably confident that I am
correct.

but as it was 12+ years ago now the odds of the test pieces still
being around are slim..

As an aside and since I can't provide the test pieces or results
anymore, the grain structure and the stress corrosion results

what did you use?

The NAS accelerated Stress corrosion test used for stainless
fasteners.. I can't remember the number for the life of me.. spokes
were pre-stressed in a fixture then underwent repeated immersion in
salt water solution at elevated temp. I attempted to compensate for the
hub rim offset..

micro-sections were done and samples were Acid etched (Oxalic?
Hydrofluoric? don't remember) / microscope showed inter-granular
corrosion (grain boundary attack what ever the correct term is)
concentrated under the spoke elbow but present as well under the head
and in the threads.

Quoted message said:

Quoted message said:

(1) and one or two tests of hubs, welds cranks etc. as I used up the
extra bits I acquired over the years.

good to hear - someone that actually did testing!!! it would be great
if you could share more detail.

I don't want people to get me wrong here I'm not an engineer I was a
technician ( a damned good one, but still) I did this for personal
interest and as practice when I was new in the job. My sample sizes
were small and could very easily have been non-representational, but
they are consistent with what other anecdotal evidence seems to show.

Quoted message said:

spokes
were pre-stressed in a fixture then underwent repeated immersion in
salt water solution at elevated temp. I attempted to compensate for the
hub rim offset..

Unfortunately, this makes these tests not say much about residual
manufacturing stress.